1955 AHSME Problem 47

The expressions a+bc and (a+b)(a+c) are:

\begin{array}{l} \textbf{(A)}\ \text{always equal}\qquad\textbf{(B)}\ \text{never equal}\qquad\textbf{(C)}\ \text{equal whenever }a+b+c=1\\ \textbf{(D)}\ \text{equal when }a+b+c=0\qquad\textbf{(E)}\ \text{equal only when }a=b=c=0 \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.